In: Accounting
Price a put option with a one-step binomial tree. Suppose So=50, X=40, 1+r=1.06. The u factor is 1.4 and the d factor is 0.6. Show the steps. (12 points)
c0= | Call price | = | [∏c1+ + (1-∏)c1- ]/ (1+r) | |
p0= | Put price | = | [∏p1+ + (1-∏)p1- ]/ (1+r) | |
Where | ||||
∏= | Risk neutral probability | = | (1+r-d)/(u-d) | |
r= | risk free interest rate | = | 6% | |
u= | up factor | = | 1.4 | |
d= | Down factor | = | 0.6 | |
∏= | Risk neutral probability | = | (1+0.06-0.6)/(1.4-0.6) | |
= | 0.5750 | |||
1- ∏= | = | 0.4250 | ||
S0 = | Stock price today | = | 50 | |
S1+ = | = 50 × 1.4 | = | 70.00 | |
S1- = | = 50 × 0.6 | = | 30.00 | |
X = | Exercise price | = | 40 | |
p1+ = | = Max(0, X - S1+) | |||
= Max(0, 40 - 70) | = | 0 | ||
p1- = | = Max(0, X - S1-) | |||
= Max(0, 40 - 30) | = | 10.0000 | ||
p0= | (0.575 × 0 + 0.425 × 10) /(1+0.06 ) | = | 4.01 |
Fair value of put option is $4.01
please rate.